Preliminary notes on the asteroid belt from Star Wars: The Empire Strikes Back.

This page will soon be re-written so that the increasing volumes of
evidence contrary to common Warsie interpretations of the event can be
properly correlated and joined into a unified argument. This page will
also include a more thorough and detailed analysis of the event than has
been performed by anyone else, to my knowledge.

Thus, this page will come to include the following:
1. Spatial analysis of the event, using photographic analysis
techniques and comparisons with other examples. This will tell us
just where everything is.
2. An examination of the question of whether or not the asteroid was
vaporized, looking at concepts including (but not limited to):
-a. asteroid composition
-b. thermal conductivity of the materials
-c. comparison to similar real-life events
-d. comparison to other similar scenes in Star Wars
(This will tell us what really happened.)
3. Comparison of my work and conclusions with the work and
conclusions of others who have examined the scene.

The rewrite should allow this to make more sense, as well, since this page
and the numerous updates and extra notes have evolved into little more
than a mass jumble of unconnected matters.

Pro-Wars debaters like to use the scene of asteroid being fired on by a
Star Destroyer in The Empire Strikes Back to claim huge firepower
estimates for turbolasers, somewhere in the range of mega-uber-gazillions
of mega-uber-google-gazilla-joules. They say the asteroids are totally
vaporized, and that the asteroids are very large.

Let's take a look at that, shall we?

Update

The "Bad Science Argument" from 'The Ambivalent DMZ':

One debater has pointed out a serious flaw in one of the most touted
calculations for asteroid-destruction firepower. *Even if* we grant the
energy levels the pro-Wars debaters generally claim for turbolasers, it is
not possible for them to have totally vaporized the asteroid, as is
claimed. Observe:

Wong's argument is a case of "bad science" rather than
"pseudoscience" - he applies some physical principles to the
calculations, and yet avoids others which could critically effect the
results. This isn't comparison shopping, folks - you can't choose
which physical laws you want to apply if you go down this road - it's
all or nothing. An analogy would be the calculations to determine a
man falling off a cliff - what speed does he have before impact? - the
answer is much higher if we forgot to account for air resistance.

Silicates have very poor thermal conductivity, even given the
(unspecified) iron content. Given the timescale over which the energy
is absorbed (1/12s), we can expect local vaporisation to occur almost
immediately. This local expansion is much greater than that required
to blast said asteroid apart.

The "blobs of superheated liquid" can only be from the area
immediately adjacent to the initial impact. The vast bulk of the
asteroid has been shattered and dispersed long before they have
absorbed sufficient energy to "visibly glow."

The "lower limit" calcs are nothing of the sort. The figure
obtained is meaningless, based on a false assumptions - namely that
the entire mass of the asteroid is vaporised, and that the energy
is absorbed uniformly and instantly throughout the entire mass
(this second assumption also flies in the face of all known physics).

DMZ

***

Quite correct.

Pro-Wars debaters attempt to override the physics
lesson mentioned above by claiming that the melting and vaporization would
be supersonic, meaning that the expansion stress on the
rock wouldn't even
have a chance to start breaking it apart before the entire rock was simply
gone.

However, this is also contradictory to physics. Impact shockwaves are
not always subsonic phenomena, unlike the normal elastic and seismic
waves that the pro-Wars debaters seem to be thinking about. (In rock on
Earth, the speed of sound (or, to use a more intuitionally valid term, the
speed of your average vibration) is going to be around three kilometers
per second, or about ten times the speed of sound in air. Solids allow
for faster vibration wave velocity, since they are more compact,
molecularly.)
For example, a meteor impact on the surface of Earth can cause pressures
of 100 GigaPascals on the target material, which will vaporize and melt
much of the surrounding target rock. What's happening there is that a
meteor strikes at a speed far greater than what the rock could transmit
elastically at the speed of sound. The kinetic energy of the meteor
therefore is moving at supersonic speeds, beyond what the rock could
otherwise tolerate. Therefore, the kinetic energy gets translated to
heat, which melts or vaporizes the immediate area of impact.
Further outward, shock pressures decrease
exponentially
as the supersonic shockwaves travels through more rock. On a planetary
impact site, shockwave pressures of 5-50 Gpa will "only" cause
metamorphism, depending on the material. 5 Gpa is the usual lower limit
for what is referred to as
the Hugoniot Elastic Limit, beyond which irreversible distortions of the
target material occur, ranging from fracture to metamorphosis of the rock
types.

It is only when the shockwave weakens to 2Gpa that the shockwaves
transition from supersonic to sonic and subsonic velocities, and become
the seismic waves we all know and love. (in progress, more details to
come)

Note: This site
has the most succinct quote in reference to something I've read repeatedly
lately about asteroids . . . that they are often mere conglomerations of
asteroidlets:

"Not long ago, astronomers thought of asteroids as rocks, perhaps
rubble covered, but still mainly single bodies. But evidence has
accumulated that asteroids are rubble piles all the way through, loosely
bound together by what is generously called "gravity" (escape velocity is
11,000 meters per second on Earth but less than 1 meter per second on a
typical small asteroid)." . . . "Crater chains on the moons
of Jupiter, on Earth's moon, and on Earth itself also point to the
gravity-induced disintegration of many asteroids prior to impact.
Asteroids which rotate fast enough to fling pieces clear are extremely
rare -- only two are known -- which suggests that these are the rare
single-rock objects."

For example, we know the densities of several asteroids in our own
solar system to a very good degree of accuracy. Some, like Eugenia, are
only 1200 kg/m3, whereas others such as Ida are in the range of
2600
kg/m3, plus or minus 600kg/m3.

This may explain the picture below, wherein asteroidlets are visible
after a collision between two asteroids. These asteroidlets are not
propelled in any particular direction, instead simply sitting there. A
loose conglomeration of material might demonstrate this, also, since
individual asteroidlets would be unlikely to impart significant velocities
on their fellows, as compared to fragments of an obliterated solid object.
This also suggests additional reason for the fragmentation of the
turbolasered asteroid.

Note: the following is unedited, and may thus appear to be something
of a "stream-of-consciousness" piece. However, it should be
understandable.

I will revise this as soon as possible.

In TESB, we see the Falcon enter an asteroid field while being pursued
by four TIE fighters. In the early phase of this, we see, outside the
cabin of the Falcon, an asteroid come flying from the right, colliding in
the upper center of the screen with a larger asteroid.

This results in a bright flash, followed by a quick, gaseous explosion
that dissipates within a scant few frames. The collision causes the total
destruction of the two asteroids, leaving only a small dust cloud and a
large number of asteroidlets that the Falcon flies through. The asteroidlets
cause no apparent damage, though they do cause a little shake.

Asteroid CollisionPicture
graciously provided by Wayne Poe

Were we to compare this to the scene in which an ISD is popping asteroids
later on, we find that the effects are remarkably similar. We observe the
destruction of an asteroid in a quick explosion that dissipates rapidly.
There are virtually no glowing embers drifting off from either destroyed
asteroid. The only debris from the explosions is seen by the Falcon, which happens to
fly through the apparently cool asteroidlets.

Asteroid PoppingPicture
graciously provided by Wayne Poe

The question is, could similar asteroidlets have resulted from the
later scene, where turbolasers are being used? Such asteroidlets would
not have been visible in the Star Destroyer scene, much as they were only
barely visible in the Falcon scene until the Falcon was going through
them. The popping scene explosion seems less detailed, somehow, possibly
due to a difference of range or scale.

Granted, there is a difference between a turbolaser hit and a hit from
a
smaller asteroid, but the energy involved can be determined in both
cases.

Unfortunately, it is difficult to get a size estimate of the Falcon's
larger asteroid (the one that was hit by the smaller). However, were we to
assume a strikee asteroid width of, say, 15 meters, we'd have a striking
asteroid of some 5 meters width (approximately).

I can make an estimate of the speed of this 5 meter asteroid. First,
I observe that the asteroid is able to move
twice it's own width per frame. Assuming 30 frames per second on my borrowed
TESB SE tape, and assuming the asteroid is five meters wide, we come to an
approximate speed of 300 meters per second, which is a fairly nice clip.

From this, we can use assumptions and some calculations to get
an estimate of the kinetic energy. For instance, if we assume
(generously) that the asteroids are made of pure iron, the mass of the
asteroid would be on the order of 515,090 kilograms.

According to my calculations, this places the kinetic energy of the
striking asteroid at 23.2 GJ. The asteroid that was struck, if 15 meters
wide, was about 25 meters top to bottom, and I assume about 15 meters thick.
Estimating it's volume with the simple length x width x height, we find that
it had a volume of about 5625 cubic meters.

This is over fifteen hundred cubic meters larger than common pro-Wars
estimates of a 20 meter diameter spherical asteroid from the ISD asteroid
scenes.

What have we found out thus far? That it took 23.2 GJ to destroy an
asteroid of 5625 cubic meters. Whoopty-doo, right? Ah, but wait . . .
the destruction of the Falcon's asteroid and the destruction of the
ISD's asteroids are remarkably similar effects. They both have the impact,
the glowing eruptions opposite the impact point, the fiery burst, and then
nothing, and all this occurs in mere fractions of a second.

Here, then, are a few issues. The ISD scene would not have shown
asteroidlets, either due to the targets being much smaller asteroids or,
alternately, the asteroids were too distant and the asteroidlets too
small. If you look at the Falcon asteroid destruction, you see an
incredibly detailed explosion, while the ISD scene only has a
non-descript gassy poof. As for the asteroidlets, one could argue that
they were only seen in the Falcon scene due to the Falcon's passage through
them . . . they were only barely seen immediately following the asteroids'
destruction, compared to the asteroids they came from.

Another issue revolves around the notion that we ought to have seen
molten or glowing fragments in the Falcon scene . . . but we don't. What
we see instead is a partial vaporization coupled with
fragmentation/shatter . . . but no glowing bits are seen.
We might then assume that either the asteroids are not iron but, instead,
something that is either vaporized or fragmented but not melted, or
alternately that the special effects team simply chose not to add molten bits.

All this applied to the ISD scene would indicate that it is entirely
likely that the asteroids popped by the turbolasers were not entirely
vaporized. If the ISD scene asteroids were on the order of 20 meters in
diameter, they could have been dismantled by around 23.2 GJ of energy.
If the ISD scene asteroids were in the 10 meter range, they could have been
dismantled by around 3.9 GJ of energy. If the ISD asteroids were in the 5
meter range, they could have been dismantled by a force of .2 GJ, or about
238 MJ. These estimates are actually rather high, considering the fact that
they are based off of the Falcon scene (where the width of the asteroid was
far less than the height). If they were lowered appropriately, we would
have figures roughly 20-25% less. To ensure fairness, I shall use both the
high and low estimates.

Converting this to watts, and assuming one-tenth of a second for
both the Falcon scene and ISD scene impacts against asteroids, we get:

(Actually, considering the fact that UVD gives .225 to .3 seconds for
the turbolaser bolts in the ISD scene to destroy the asteroids, these
figures are also terribly high. To correct the appropriately lowered
estimates, we'd find figures of 57-76 GW, 10-13 GW, and .6-.8 GW (600 to
800 MW) respectively.)

None of these figures, high or low, put the turbolaser cannons in the
terawatt range, as some of the more vigorous pro-Wars debaters do.
Indeed, these watt figures refer to the power of an
individual turbolaser bolt . . . to determine the power output of a
turbolaser cannon over sustained periods, we'd need to know the recharge
time. From the "Turbolaser Commentaries" analysis of recharge time, we
get the figure of two seconds. We thus find the following:

Now the most important question that remains is, how big are the
asteroids that the ISD was popping? This, unfortunately, can be a matter
of serious contention. We are not given the camera's distance from
either the ISD or the asteroids, nor are we given any idea of the
camera's field of view. We do not know the distance from the ISD to the
asteroids.

However, we do know a few things. We do know that, assuming the
ISD is moving forward along her own orientation, the camera is not in the
path of the ship. We do know that, assuming the ISD is moving forward
along her own orientation, that the largest soon-to-be-popped asteroid
visible (the one apparently closest to the camera) at the beginning of
that scene is moving from port toward starboard, from the ISD's point of
view (i.e. it's coming in from a 10 or 11 o'clock angle when it's popped).
This is corroborated by the fact that, later, we see an ISD firing on the
Millennium Falcon that is directly in front of her, and the ISD looks
almost exactly the same insofar as angle and distance are concerned.
The turbolaser bolts fired toward the Falcon are extremely thin from the
camera's vantage point . . . the turbolaser bolts fired at the asteroids
are much thicker. When we see the view from the Millennium Falcon
directly astern, the beams appear much thicker. This either implies that
turbolasers have power settings (low for MF, high for asteroids) that
changed when the camera was looking back from the Millennium Falcon, or (
more likely in this case) that the ISD popping asteroids was firing
more in the camera's direction, thus making thicker-looking bolts
(just as the pencil-thin bolts appeared much thicker when viewed from a
better angle).

We can try several things here. We can guess, based on the path of the
asteroid and it's apparent closeness in the beginning of the
ISD-pops-asteroids scene, what it's size is. Or, we can attempt to use the
TL bolt that appears to have struck the Millennium Falcon's hull in the
chase scene to determine the width of a turbolaser bolt. For the latter,
assuming a 30-meter wide Falcon, we find that turbolaser bolts are, at
best, 1-1.5 meters wide. This seems corroborated by the shot from the side
with the pencil-thin TL bolts a few moments earlier.

Turbolaser Bolt about to hit Millennium Falcon

Applying this width to the TL bolts in the popping scene, we find that
the main asteroid is no more than three to five meters in diameter. This
still leaves it at between ten and fifteen feet, roughly, which is none too
shabby. This gives us a lower sustained firepower estimate for a turbolaser
of 22-29 MW assuming a 3 meter main asteroid, 90-120 MW assuming a five
meter asteroid. Of course, in both those ranges, the upper figures
(29 and 120) are not appropriately lowered, as per previous statements.

Of course, we do not know how long a turbolaser cannon can continue
engaging in sustained fire, firing a bolt every two seconds. We do know,
however, that there are sixty such turbolaser cannons aboard an ISD,
according to many various sources. Assuming that forty of these, on
average, can be trained on any one vessel at any one time, we find that a
Star Destroyer is capable of between 880 MW and 3600 MW (3.6 GW) sustained
fire on a target, assuming that all bolts hit their mark.

These estimates are also quite high, considering the fact that we have
assumed asteroids of solid iron. The Official Star Wars Web Site states
that "The dangerous asteroid belt in the Hoth system was formed billions
of years ago by the collision of two planets. Millions of boulders and
rocky asteroids careen through space in orbit together, forming a deadly
swarm and a menace to navigation."

This would seem to imply that the asteroids are predominately composed of
rock, not pure metal. We do not know the composition of this rock,
unfortunately, but if one were to guesstimate the density of this rock by
using the density of the entire moon as an example, we'd have asteroids less
than half as dense as iron (3300 kg/m3 as opposed to the
7924.5 kg/m3
used for iron).

Let us, then, estimate the required energy to produce the shatter and
partial vaporization of various sized asteroids, assuming they are made of
rock and not iron:

And now, assuming 40 turbolaser cannons could be fired at a vessel and
all bolts would hit, we have a sustained power of between 2 GW and 200 GW.
However, using the previous argument that the ISD's main visible asteroid
was between 3 and 5 meters in diameter, we find that the sustained
firepower of an ISD is 2 GW or below . . . perhaps as low as 800 MW for
the whole ship.

Of course, this is based on the density of Earth's moon. In fact, that
density might be far too high. To our own local asteroids, we have sent a
NASA probe. This probe's data shows that one asteroid, 253 Mathilde, has a
density of only 1.3 g/cm^3, or about 1300 kg/m^3. As a C-type asteroid, this
is to be expected . . . it's predominately carbon. The asteroid 433 Eros,
S-type, has a density of about 2600 kg/m3. It is predominately composed of
high concentrations of silicate materials and metal. An estimate of average
asteroid density might be 2000 kg/m3.

And now, using the five-meter ISD main asteroid hypothesis, coupled with
the forty-TL on one target figure, we find that the firepower of a Star
Destroyer against a target is on the order of 1.2 GW . . . if the asteroid
was three meters, then the Star Destroyer would have something like
500 MW per forty turbolasers, all bolts of which must hit the target.

Meanwhile, pro-Wars debaters float theories and calculations suggesting
that the asteroid was larger and completely vaporized in an instant
(despite the contradiction with physical laws) with lower-limit
*per bolt* estimates of 31,000 terajoules! The maximum I could come up
with was a mere 23.2 gigajoules, making their estimates * 1.3 million
times* my own. That's preposterous.

Even if we grant the erroneous assumption made by some pro-Wars
debaters (based on one interpretation of the non-canon TNG Technical
Manual) that
the dorsal phaser array on the saucer of the Enterprise-D is only capable
of directing 1.02 GW against shields, that array alone is about as powerful
as a Star Destroyer's turbolaser complement, if not more powerful.

Something worth noting here, though, is the fact that the phase cannons
aboard Enterprise NX-01 are rated at 500 gigajoules per shot, according to
Reed in "Silent Enemy"[ENT]. Even allowing for larger asteroids of solid
iron, phasers are much more powerful than turbolasers.

Update: Many Warsie debaters will try to claim asteroid sizes greater
than 20 meters. However, this cannot be so. Take a look at the
following two screen caps:

Falcon being pursued by ISD

ISD firing
at asteroids

As you can see, the Falcon is being fired on in the first shot. The
scene makes it clear that the Falcon is almost directly in front of the
ISD. The Falcon's size is generally estimated to be a maximum of
40 meters in length. The scene which features the ISD firing on the
asteroids has the ISD at almost exactly the same lateral angle from our
perspective (look at the starboard point compared to the forward point in
both images), but firing more toward the camera (about 30 degrees off the
forward axis). The firing angle, plus
the trajectory of the asteroid, plus the distance of the asteroid from
the ship, plus the thickness of the beam, all serve to
make it readily apparent that the ISD is firing much further toward her port
side than in the forward-shooting Falcon chase.

Therefore, the chase scene constrains the possible size of the
asteroid to less than forty meters, since it could not possibly have
appeared as large as the Falcon did when it was in front of the ISD.

More on this issue will come soon.

(Notes)

Normal lightning bolts are rated at between 1 and 10 gigajoules,
though a very significant fraction of that energy is radiated by the heat,
light, and shockwave before it ever hits the ground.